Advances in light source technology, such as, for example, light-emitting diode (LED) technology, have led to very bright and reliable solid state lamps. However, challenges remain with respect to coupling LEDs to optical transmission media, such as, for example, optical rods and optical tapers. While there have been numerous attempts to utilize low power (<1 W electrical power consumption, typically operating below 100 mW) light-emitting diodes (LEDs) coupled to fiber optic light guides or other optical devices as light sources for endoscopy, dentistry, and for remote illumination of objects (as with a flashlight, head light, or lamp), most of these prior attempts have employed numerous low power LEDs for remote illumination. Generally, multiple LEDs are necessary because the light output from a single, low power LED is typically too weak to properly illuminate an object. In addition, the arrangement of the multiple LEDs to the optical transmission media used in these prior attempts has resulted in unacceptable light loss, thereby further decreasing the low power LED's ability to properly illuminate an object.